Models for surface gravity wave propagation in the presence of currents often assume the current field to be quasi-stationary, which implies that the absolute wave frequency is time invariant. However, in the presence of unsteady currents or time-varying water depth, linear wave theory predicts a time variation of the absolute wave frequency (and wavenumber). Herein, observations of wave frequency modulations from a large-scale laboratory experiment are presented. In this case, the modulations are caused by both unsteady depths and unsteady currents due to the presence of low-frequency standing waves. These new observations allow a unique and detailed verification of the theoretical predictions regarding variations in the absolute wave frequency. In addition, analytic solutions for the variations in frequency and wave height induced by the unsteady medium are found through a perturbation analysis. These solutions clarify the dependency of the wave frequency/wave height modulations on the characteristics of the unsteady medium. We also find that analytic solutions for simplified basin configurations provide an order of magnitude estimate of the expected frequency modulation effect. Finally, the importance of this phenomenon in natural situations is discussed.
A numerical model is presented that predicts the evolution of a directional spectral sea state over a varying bathymetry using superposition of results of a parabolic monochromatic wave model run for each initial frequency-direction component. The model predicts dissipation due to wave breaking using a statistical breaking model and has been tested with existing data for unidirectional random waves breaking over a plane beach. Experiments were also conducted for a series of random directional waves breaking over a circular shoal to test the model in a two-dimensional wave field. The model performs well in both cases, although directional effects are not included in the breaking dissipation formulation.
Abstract Interest in validating the eddy covariance (EC) technique under wave-induced flows led to a series of experiments in a 104-m-long large wave flume (LWF) using an acoustic Doppler velocimeter (ADV) and two oxygen microelectrodes (tips ~2 mm apart) mounted on a sturdy tripod. Four additional ADVs positioned within the flume provided comparative near-bed velocity measurements during experiments with irregular waves over a sand bed. These measurements revealed that modifications of local turbulence by the tripod frame were insignificant. However, errors in velocity measurements were at times observed for setups where the microelectrode tips protruded into the ADV’s measurement volume. Disparate oxygen microelectrode velocity effects (stirring sensitivities) combined with response time offsets were also identified as problems, adding biases to EC flux derivations. Microelectrode velocity effects were further investigated through modeling designed to mimic the LWF data, and through examination of a 12-h dataset from the Oregon shelf. The modeling showed that under progressive waves, an artificial EC flux, or bias, arises most severely when the velocity sensitivity of the microelectrode is unequal in opposing flow directions or augmented by horizontal currents, and the velocity and oxygen data are not perfectly aligned in time. Sensitivities to wave motions were seen in the oxygen measurements from the Oregon shelf, contributing to an average flux of +2.7 ± 0.6 mmol m −2 day −1 (SE, n = 22) at wave frequencies. Since overall EC fluxes equaled only −4.1 ± 1.8 mmol m −2 day −1 (SE, n = 22), sources of EC biasing coupled to waves cannot be ruled out as potential problems for estimating exact benthic oxygen fluxes under common continental shelf field conditions.
Abstract An operational inner-shelf wave forecasting system was implemented for the Oregon and southwest Washington coast in the U.S. Pacific Northwest (PNW). High-resolution wave forecasts are useful for navigational planning, identifying wave energy resources, providing information for site-specific coastal flood models, and having an informed recreational beach user group, among other things. This forecasting model is run once a day at 1200 UTC producing 84-h forecasts. A series of nested grids with increasing resolution shoreward are implemented to achieve a 30-arc-second resolution at the shelf level. This resolution is significantly higher than what the current operational models produce, thus improving the ability to quantify the alongshore variations of wave conditions on the PNW coast. Normalized root-mean-squared errors in significant wave height and mean wave period range from 0.13 to 0.24 and from 0.13 to 0.26, respectively. Visualization of the forecasts is made available online and is presently being used by recreational beach users and the scientific community. A series of simulations, taking advantage of having a validated shelf-scale numerical wave model, suggests that neither dissipation due to bottom friction nor wind generation is important in the region at this scale for wave forecasting and hindcasting when considering bulk parameters as opposed to the processes of refraction and shoaling. The Astoria and McArthur Canyons; the Stonewall, Perpetua, and Heceta Banks; and Cape Blanco are significant bathymetric features that are shown to be capable of producing alongshore variability of wave heights on the shelf.
Abstract The three‐dimensional (across‐shore, alongshore, and vertical) structure of hourly mean currents and <0.01 Hz eddies was measured on a natural beach using 12 Acoustic Doppler Profilers. Both eddies and alongshore currents became relatively depth‐uniform inside the surfzone. Eddies showed greater depth dependence than alongshore currents. A two‐layer model, derived by scaling of the wave‐averaged shallow water equations, yielded separate equations for depth‐averaged and depth‐dependent velocity components. Scaling suggests, and observations confirm, only a small role for lateral advection in most surfzone cases, leading to one‐dimensional vertical models for depth dependence. For alongshore currents, depth dependence is generated by opposite forcing on lower and upper layers, respectively by bottom friction (quantified by time scale ) and waves or wind. This generation is balanced by mixing between upper and lower layers (time scale ), so the ratio between depth‐dependent and depth‐averaged alongshore currents equals . Established models for bottom friction and breaker‐induced mixing predicted a surfzone reduction in consistent with the observed reduction in alongshore current depth dependence. Scatter around trends was considerable. Alongshore variability was significant for depth‐dependence of currents and eddies. Inside (but not outside) the surfzone, the mixing time scale was shorter than the eddy period, so a quasi‐steady balance was predicted between forcing and mixing of eddy depth dependence. Observed eddy depth dependence exceeded predictions for barotropic eddies generated by shear production (i.e., shear instabilities), possibly indicating generation of eddies by random breaking waves in the surfzone, or indicating baroclinic effects outside the surfzone.